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目錄
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0 A Precalculus Review
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8 |
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1 Functions, Graphs, and Limits
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9 |
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Section 1.2 Graphs of Equations
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10 |
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Section 1.3 Lines in the Plane and Slope
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11 |
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Section 1.4 Functions
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12 |
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Section 1.5 Limits
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13 |
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Section 1.6 Continuity
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14 |
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2 Differentiation
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15 |
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Section 2.2 Some Rules for Differentiation
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16 |
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Section 2.3 Rates of Change: Velocity and Marginals
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17 |
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Section 2.4 The Product and Quotient Rules
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Section 2.5 The Chain Rule
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19 |
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Section 2.6 Higher-Order Derivatives
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20 |
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Section 2.7 Implicit Differentiation
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21 |
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Section 2.8 Related Rates
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22 |
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Algebra Review
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3 Applications of the Derivative
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Section 3.2 Extrema and the First-Derivative Test
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Section 3.3 Concavity and the Second-Derivative Test
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26 |
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Section 3.4 Optimization Problems
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Section 3.5 Business and Economics Applications
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Section 3.6 Asymptotes
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Section 3.7 Curve Sketching: A Summary
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30 |
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Section 3.8 Differentials and Marginal Analysis
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31 |
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Algebra Review
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32 |
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4 Exponential and Logarithmic Functions
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33 |
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Section 4.2 Natural Exponential Functions
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34 |
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Section 4.3 Derivatives of Exponential Functions
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35 |
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Section 4.4 Logarithmic Functions
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Section 4.5 Derivatives of Logarithmic Functions
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Section 4.6 Exponential Growth and Decay
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38 |
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Algebra Review
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5 Integration and Its Applications
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40 |
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Section 5.2 Integration by Substitution and the General Power Rule
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41 |
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Section 5.3 Exponential and Logarithmic Integrals
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42 |
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Section 5.4 Area and the Fundamental Theorem of Calculus
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43 |
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Section 5.5 The Area of a Region Bounded by Two Graphs
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44 |
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Section 5.6 The Definite Integral as the Limit of a Sum
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45 |
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Algebra Review
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46 |
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6 Techniques of Integration
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47 |
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Section 6.2 Partial Fractions and Logistic Growth
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48 |
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Section 6.3 Integration Tables
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49 |
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Section 6.4 Numerical Integration
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50 |
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Section 6.5 Improper Integrals
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51 |
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7 Function of Several Variables
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Section 7.2 Surfaces in Space
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53 |
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Section 7.3 Functions of Several Variables
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54 |
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Section 7.4 Partial Derivatives
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Section 7.5 Extrema of Functions of Two Variables
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Section 7.6 Lagrange Multipliers
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Section 7.7 Least Squares Regression Analysis
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Section 7.8 Double Integrals and Area in the Plane
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Section 7.9 Applications of Double Integrals
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60 |
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8 Trigonometric Functions
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61 |
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Section 8.2 The Trigonometric Functions
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62 |
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Section 8.3 Graphs of Trigonometric Functions
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63 |
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Section 8.4 Derivatives of Trigonometric Functions
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64 |
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Section 8.5 Integrals of Trigonometric Functions
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65 |
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9 Probability and Calculus
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66 |
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Section 9.2 Continuous Random variables
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67 |
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Section 9.3 Expected Value and variance
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68 |
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10 Series and Taylor Polynomials
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69 |
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Section 10.2 Series and Convergence
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70 |
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Section 10.3 ρ-Series and the Ratio Test
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71 |
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Section 10.4 Power Series and Taylor's Theorem
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72 |
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Section 10.5 Taylor Polynomials
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73 |
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Section 10.6 Newton's Method
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74 |
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Appendices
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75 |
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B Formulas
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76 |
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C Differential Equations
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77 |
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C.2 Separation of Variables
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78 |
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C.3 First-Order Linear Differential Equations
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79 |
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C.4 Applications of Differential Equations
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80 |
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Answer to Selected Exercises
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